/// \file
/// \ingroup tutorial_math
/// \notebook
/// Tutorial illustrating the use of the Student and F distributions
///
/// \macro_image
/// \macro_code
///
/// \author Anna Kreshuk

#include "TMath.h"
#include "TF1.h"
#include "TCanvas.h"
#include <Riostream.h>
#include "TLegend.h"
#include "TLegendEntry.h"

void mathStudent()
{
   //drawing the set of student density functions
   //normal(0, 1) density drawn for comparison
   TCanvas *DistCanvas = new TCanvas("DistCanvas", "Distribution graphs", 10, 10, 800, 650);
   DistCanvas->SetFillColor(17);
   DistCanvas->Divide(2, 2);
   DistCanvas->cd(1);
   gPad->SetGrid();
   gPad->SetFrameFillColor(19);
   TLegend *leg = new TLegend(0.6, 0.7, 0.89, 0.89);


   TF1* fgaus = new TF1("gaus", "TMath::Gaus(x, [0], [1], [2])", -5, 5);
   fgaus->SetTitle("Student density");
   fgaus->SetLineStyle(2);
   fgaus->SetLineWidth(1);
   fgaus->SetParameters(0, 1, kTRUE);
   leg->AddEntry(fgaus->DrawCopy(), "Normal(0,1)", "l");

   TF1* student = new TF1("student", "TMath::Student(x,[0])", -5, 5);
   //student->SetTitle("Student density");
   student->SetLineWidth(1);
   student->SetParameter(0, 10);
   student->SetLineColor(4);
   leg->AddEntry(student->DrawCopy("lsame"), "10 degrees of freedom", "l");

   student->SetParameter(0, 3);
   student->SetLineColor(2);
   leg->AddEntry(student->DrawCopy("lsame"), "3 degrees of freedom", "l");

   student->SetParameter(0, 1);
   student->SetLineColor(1);
   leg->AddEntry(student->DrawCopy("lsame"), "1 degree of freedom", "l");

   leg->Draw();

   //drawing the set of student cumulative probability functions
   DistCanvas->cd(2);
   gPad->SetFrameFillColor(19);
   gPad->SetGrid();
   TF1 *studentI = new TF1("studentI", "TMath::StudentI(x, [0])", -5, 5);
   studentI->SetTitle("Student cumulative dist.");
   studentI->SetLineWidth(1);
   TLegend *leg2 = new TLegend(0.6, 0.4, 0.89, 0.6);

   studentI->SetParameter(0, 10);
   studentI->SetLineColor(4);
   leg2->AddEntry(studentI->DrawCopy(), "10 degrees of freedom", "l");

   studentI->SetParameter(0, 3);
   studentI->SetLineColor(2);
   leg2->AddEntry(studentI->DrawCopy("lsame"), "3 degrees of freedom", "l");

   studentI->SetParameter(0, 1);
   studentI->SetLineColor(1);
   leg2->AddEntry(studentI->DrawCopy("lsame"), "1 degree of freedom", "l");
   leg2->Draw();

   //drawing the set of F-dist. densities
   TF1* fDist = new TF1("fDist", "TMath::FDist(x, [0], [1])", 0, 2);
   fDist->SetTitle("F-Dist. density");
   fDist->SetLineWidth(1);
   TLegend* legF1 = new TLegend(0.7, 0.7, 0.89, 0.89);

   DistCanvas->cd(3);
   gPad->SetFrameFillColor(19);
   gPad->SetGrid();

   fDist->SetParameters(1, 1);
   fDist->SetLineColor(1);
   legF1->AddEntry(fDist->DrawCopy(), "N=1 M=1", "l");

   fDist->SetParameter(1, 10);
   fDist->SetLineColor(2);
   legF1->AddEntry(fDist->DrawCopy("lsame"), "N=1 M=10", "l");

   fDist->SetParameters(10, 1);
   fDist->SetLineColor(8);
   legF1->AddEntry(fDist->DrawCopy("lsame"), "N=10 M=1", "l");

   fDist->SetParameters(10, 10);
   fDist->SetLineColor(4);
   legF1->AddEntry(fDist->DrawCopy("lsame"), "N=10 M=10", "l");

   legF1->Draw();

   //drawing the set of F cumulative dist.functions
   TF1* fDistI = new TF1("fDist", "TMath::FDistI(x, [0], [1])", 0, 2);
   fDistI->SetTitle("Cumulative dist. function for F");
   fDistI->SetLineWidth(1);
   TLegend* legF2 = new TLegend(0.7, 0.3, 0.89, 0.5);

   DistCanvas->cd(4);
   gPad->SetFrameFillColor(19);
   gPad->SetGrid();
   fDistI->SetParameters(1, 1);
   fDistI->SetLineColor(1);
   legF2->AddEntry(fDistI->DrawCopy(), "N=1 M=1", "l");

   fDistI->SetParameters(1, 10);
   fDistI->SetLineColor(2);
   legF2->AddEntry(fDistI->DrawCopy("lsame"), "N=1 M=10", "l");

   fDistI->SetParameters(10, 1);
   fDistI->SetLineColor(8);
   legF2->AddEntry(fDistI->DrawCopy("lsame"), "N=10 M=1", "l");

   fDistI->SetParameters(10, 10);
   fDistI->SetLineColor(4);
   legF2->AddEntry(fDistI->DrawCopy("lsame"), "N=10 M=10", "l");

   legF2->Draw();
   DistCanvas->cd();
}
